Related papers: The Effective Number of Parameters in Kernel Densi…
All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and…
We present fully empirical exchange-correlation functionals to be used within reduced density matrix functional theory (RDMFT). These are of the popular J-K form, where the function of the occupation numbers that multiplies the Fock orbital…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
We introduce a new deal of kernel density estimation using an exponentiated form of kernel density estimators. The density estimator has two hyperparameters flexibly controlling the smoothness of the resulting density. We tune them in a…
Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is…
Density functional theory (DFT) is the de facto approach for predicting self-consistent-field electronic structures of ground-state configurations of complex atoms, molecules, and solids and providing their property data for materials…
A key ethical challenge in Automated Essay Scoring (AES) is ensuring that scores are only released when they meet high reliability standards. Confidence modelling addresses this by assigning a reliability estimate measure, in the form of a…
We consider optimization problems that arise when estimating a set of unknown parameters from experimental data, particularly in the context of nuclear density functional theory. We examine the cost of not having derivatives of these…
This paper proposes the first generic fast convergence result in general function approximation for offline decision making problems, which include offline reinforcement learning (RL) and off-policy evaluation (OPE) as special cases. To…
Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential…
We present the simplest nuclear energy density functional (NEDF) to date, determined by only 4 significant phenomenological parameters, yet capable of fitting measured nuclear masses with better accuracy than the Bethe-Weizs\"acker mass…
We introduce a new mean-field ODE and corresponding interacting particle systems (IPS) for sampling from an unnormalized target density. The IPS are gradient-free, available in closed form, and only require the ability to sample from a…
In one-dimensional density estimation on i.i.d. observations we suggest an adaptive cross-validation technique for the selection of a kernel estimator. This estimator is both asymptotic MISE-efficient with respect to the monotone oracle,…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
As the third paper in a series regarding the estimation of luminosity functions (LFs) via kernel density estimation (KDE), we present a further generalization of our framework by extending its applicability to multiple flux-limited samples.…
When estimating target parameters in nonparametric models with nuisance parameters, substituting the unknown nuisances with nonparametric estimators can introduce ``plug-in bias.'' Traditional methods addressing this suboptimal…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…